Selection Procedures in Competitive Admission

Two identical firms compete to attract and hire from a pool of candidates of unknown productivity. Firms simultaneously post a selection procedure which consists of a test and an acceptance probability for each test outcome. After observing the firms' selection procedures, each candidate can apply to one of them. Firms can vary both the accuracy (Lehmann, 1988) and difficulty (Hancart, 2024) of their test. The firms face two key considerations when choosing their selection procedure: the statistical properties of their test and the selection into the procedure by the candidates. I show that there is a unique symmetric equilibrium where the test is maximally accurate but minimally difficult. Intuitively, competition leads to maximal but misguided learning: firms end up having precise knowledge that is not payoff relevant. I also consider the cases where firms face capacity constraints, have the possibility of making a wage offer and the existence of asymmetric equilibria where one firm is more selective than another.